Pakistan, seeking consolation from a trip that will be best remembered for corruption allegations and off-field issues, was bowled out under the lights for 135 in 37 overs, chasing 257 for victory, to lose an ill-tempered series 3-2. Pakistan also lost the test series 3-1 and the twenty/20 series 2-0.
Pakistan crashed from 63 without loss to 104-6 and failed to recover thereafter, as offspinner Graeme Swann led the way with figures of 3-26 in nine overs.
Morgan earlier scored an unbeaten 107 off 101 deliveries, and helped take 19 runs from the 50th over, for his second unbeaten hundred on the ground this year after his match-winning 103 against Australia. Fast bowler Shoaib Akhtar impressed with 3-40 from his 10 overs.
"It's been difficult, there's been a lot of distractions around, especially in the last two games," Morgan said. "Today showed how focused we were and how determined we were to win the series, and finish the summer on a high."
England captain Andrew Strauss added: "Having been 2-0 up in the series and cosy about things, it's a bit of a shock to the system to suddenly be 2-2 - especially given what went on over the last week. So we had to switch on pretty quickly, and make sure we came out in exactly the right sort of mindset today."
The result brings to an end a troubled tour for Pakistan.
"I was thinking about some happy ending but it's not happened," Pakistan captain Shahid Afridi said. "Every day there has been some controversies on this tour but I'm very happy in this situation that the team was very united and we played as a team.
"Maybe it will give us a good result in the future. Our unity is the one positive thing I am taking from the UK."
Three of Pakistan's players were suspended by the International Cricket Council on corruption charges earlier this month. The ill-feeling progressed further when Pakistan Cricket Board chairman Ijaz Butt alleged on Sunday that England lost Friday's third one-day international at The Oval on purpose. England's players were incensed by the slur and are considering legal action.
The hosts were jolted early at a packed Rose Bowl, losing three wickets for 16 runs to slump to 47-3 after being 31 without loss. It was effectively 59-4 when Collingwood was forced to retire with a migraine on 5.
Jonathan Trott, averaging 70 in one-day internationals at the start of the series, continued a downturn in form by following scores of 2 and 4 with a 3. He was bowled by a quick delivery from Akhtar that swung into him.
It was the latest blow for Trott after he was accused of striking Pakistan reserve Wahab Riaz in a training ground altercation at Lord's on Monday, though match officials did not take any action after speaking to both players.
Akhtar added the wicket of Strauss, who was hit in the stomach by a bouncing Akhtar ball in the first over. He was caught behind for 25 after playing and missing several times to similar balls that went past his outside edge.
Collingwood scored 47 and put on 93 with Morgan after earlier retiring hurt with a migraine. England's Ian Bell, in his second game back after recovering from a broken foot, had to use a runner from 14 after injuring his groin.
Morgan, who characteristically manoeuvred the ball expertly into the gaps, was dropped on 31 when Mohammed Yousuf took the catch at long-on from Hafeez but threw the ball to the ground as his momentum took him over the boundary.
Yousuf trod on the boundary rope, twisting his ankle, fell on an advertising board and was forced to leave the field for treatment. He later batted with a runner after aggravating the injury.
Morgan raised the tempo late on and reached his century in the final over by lifting Saeed Ajmal for a straight six before then driving another boundary down the ground for the milestone.
Only opener Kamran Akmal provided much resistance to England with his 41 before he was given lbw to Luke Wright, though replays showed he had got an inside edge.
Swann wrecked the Pakistani middle-order by bowling Fawad Alam with a sharp turner, and later took two wickets in two balls, bowling Mohammed Yousuf while Afridi played on first ball.
England won the first two games before Pakistan drew level through wins at The Oval and Lord's.
